We propose a novel adaptive approximation approach for test-time resource-constrained prediction. Given an input instance at test-time, a gating function identifies a prediction model for the input among a collection of models. Our objective is to minimize overall average cost without sacrificing accuracy. We learn gating and prediction models on fully labeled training data by means of a bottom-up strategy. Our novel bottom-up method first trains a high-accuracy complex model. Then a low-complexity gating and prediction model are subsequently learned to adaptively approximate the high-accuracy model in regions where low-cost models are capable of making highly accurate predictions. We pose an empirical loss minimization problem with cost constraints to jointly train gating and prediction models. On a number of benchmark datasets our method outperforms state-of-the-art achieving higher accuracy for the same cost.
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